This could have been the afternoon when Manchester City lost all real hope of winning the Premier League but instead they emerged from Sunday’s hectic back-to-back matches with transformed fortunes, now just three wins away from an unlikely title.

It was a remarkable few hours, starting with Chelsea doing what City could not by beating Liverpool at Anfield. That result re-opened the opportunity for City and, with a ruthlessness they have not always shown this season, they seized it immediately. Edin Dzeko scored after four minutes and that was more or less that.

If they win at Goodison Park on Saturday – the next classic in a season full of them – before beating Aston Villa and West Ham United at the Etihad Stadium, only an implausible flood of Liverpool goals can stop them from regaining the title they won in 2011-12. City must be slight favourites to do it, which is surprising enough given that it was just two weeks ago that Vincent Kompany miskicked and Philippe Coutinho pounced for Liverpool, sending City dazed into their game with Sunderland in which they seemed to fritter away any remaining plausible challenge with a 2-2 draw.

City, though, have a surprising capacity for both mental fragility and resilience. Had Liverpool beaten Chelsea then they might well have wilted here against Crystal Palace. The City players, though, saw the game on the big screen overlooking the Whitehorse Lane Stand as they were warming up. Sergio Aguero could barely tear his eyes away from it when the players went back to the dressing room. When this match started, then, City knew that they had a title to go and win, and, with more focus than they have summoned for some time, they set about doing just that.

Manuel Pellegrini said he “told the players not to be thinking about the Liverpool result” but City seemed to use it as a positive. Tony Pulis, the Palace manager, knew it gave City a “massive lift”.

It took just four minutes for City to take the lead. Yaya Touré found space on the edge of the box, surveyed his options and curled a perfect cross between Adrian Mariappa and Scott Dann and on to Dzeko’s forehead. Dzeko celebrated with the City fans like he knew just how much the goal might mean.

This was a performance of mature application from City’s senior players, who showed that they still have what it takes to win. Chief among them all was Touré, who was close to his decisive best on his return from injury, still not fully fit after just two days back training. His assist for Dzeko was more than good enough but his goal, just before half-time, was astounding.

Touré, breaking from half-way, held off Yannick Bolasie, played a one-two with Dzeko, burst away from Joel Ward, exchanged short sharp passes with Samir Nasri, pushed off Damien Delaney, carried on beyond Scott Dann and placed the ball with his nominally weaker left foot into the far top corner. It was Touré’s 19th goal of the league season and probably his best.

Early in the second half Touré curled one shot over the bar but was soon withdrawn for Fernandinho, and as he left the pitch the applause was not just coming from the away fans. Pulis conceded that it was a “really big disappointment” that Touré was fit enough to start. “To think that he has been out for a few weeks and can play like that,” he sighed, “he was fantastic, putting in a performance like that.”

City conserved energy as they saw the game out, and if they win their next match, at Goodison, they will go top – at least for a few hours – for the first time since January. “We must win the next three games,” Pellegrini said afterwards. “We are thinking about beating Everton next week. We must win all our games. That is important.”

Palace, for their part, did not do very much wrong. A few months ago they might have looked at this fixture with some apprehension, but to their credit they had already rendered it irrelevant with their recent form. They are no longer playing for safety – just position and pride – but never were never able to get into the game.

Pulis has done brilliant work at Selhurst Park, but his reactive counter-attacking game is less effective when Palace are losing. Only against Swansea and Norwich have Palace won back points from losing positions this season. Once Dzeko had put City ahead here, Palace never looked like adding to that tally.

Despite a few spells of possession, the home side’s threat never amounted to anything more than a simple cross or a hopeful ball into the channels. Vincent Kompany and Martin Demichelis were rarely threatened. The first serious save Joe Hart had to make, from Jason Puncheon’s 20-yard shot, was soon after the re-start, with City were already 2-0 up.

The introductions of Dwight Gayle and Glenn Murray halfway through the second half altered the atmosphere more than they changed the game. With two minutes left, Murray spun and shot, forcing Demichelis to block, but that was the extent of it.

Pulis was disappointed with the defeat but conceded that “half of my players did not play at their maximum today”. They have a chance to atone for this next Monday against Liverpool, their last home game of the season. City will probably be watching.

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